After a jury-waived trial in the Quincy District Court, the defendant was found guilty on a complaint charging him with indecent assault and battery on a person over the age of fourteen. See G. L. c. 265, § 13H. The defendant had presented an expert witness who testified that, in his opinion, the defendant had “substantial difficulties” conforming his behavior to the requirements of the law. See Commonwealth v. McHoul, 352 Mass. 544, 547 (1967).1 Insanity having been *551raised as a defense, it became the Commonwealth’s burden to prove the defendant sane beyond a reasonable doubt. Commonwealth v. Kostka, 370 Mass. 516, 526 (1976). It offered no direct evidence of sanity, and the sole question on appeal is whether the Commonwealth satisfied its burden with permissible inferences available from the evidence of the “facts underlying the crime and evidence of [the defendant’s] actions before and after the crime,” Commonwealth v. Cullen, 395 Mass. 225, 229 (1985), and with additional support from the presumption of sanity. See Commonwealth v. Kostka, 370 Mass. at 530.2 Because we conclude that the Commonwealth failed to establish beyond a reasonable doubt that the defendant was criminally responsible for his act, we reverse the judgment and order entry of a judgment of acquittal on that basis.
1. The standard of review. We note at the outset that the defendant did not request a required finding of not guilty on the basis that the Commonwealth had failed in its burden of proving his sanity. However, we treat him as if he had, for if he would have succeeded on such a motion, had it been made, to affirm his conviction would leave a substantial risk of a miscarriage of justice. See Commonwealth v. McGovern, 397 Mass. 863, 867-868 (1986) (“[findings based on legally insufficient evidence are inherently serious enough to create a substantial risk of a miscarriage of justice”). We, therefore, proceed as if the defendant had moved for a required finding at the close of all the evidence.3
*5522. The evidence. As noted, the Commonwealth offered no expert testimony concerning the defendant’s criminal responsibility. It argues on appeal that it sustained its burden of proof on the basis of the testimony of its witnesses and the presumption, or inference, of sanity. The trial was brief, and we relate all the testimony.
According to the testimony of the victim, on or about November 21, 1996, a man she did not know, the defendant, boarded a moderately crowded Massachusetts Bay Transportation Authority (MBTA) train at a time when people were traveling home from work, sat diagonally across from her, and, for about twenty minutes, stared at her while making obscene gestures and touching his clothes in the genital area, and saying, “Oh baby, you’re nice.” She did not react to his conduct or acknowledge his presence and, instead, feigned being engrossed in her book. When the victim arrived at her destination and attempted to disembark from the train, the defendant lunged for her, pushed her against the car doors of the train, groped her, and uttered obscenities, “I want you. I want to fuck you.” As the car doors opened and the victim broke to run, the defendant told her, “I’m gonna get you.” As she ran from the train to summon police assistance, a man grabbed and held the defendant on the station platform. From what the victim could see as she ran, the man appeared as if he were going to punch the defendant. When she quickly returned with three uniformed MBTA officials, the defendant offered them no resistance.
MBTA officer Miguel Rosario testified that he, another MBTA officer, and an MBTA inspector, all three in uniform, arrested the defendant. He was cooperative and his arrest uneventful. Rosario also recounted that the defendant, during the booking process immediately following his arrest, was docile and responsive to questions concerning his personal history.
At the conclusion of the Commonwealth’s evidence, the defendant called Dr. Paul Nestor, a licensed psychologist, who was a designated forensic psychologist for the Department of Mental Health and an assistant professor of psychology at the Harvard Medical School, to offer his opinion relative to the defendant’s criminal responsibility. Throughout his testimony, *553Dr. Nestor testified at length about information contained in the defendant’s hospital records from Bridgewater State Hospital (Bridgewater). As related by Dr. Nestor, the contents of the records provided additional information concerning the defendant’s conduct immediately following his arrest and booking.4
It appears from Dr. Nestor’s account of the contents of the records that when the defendant was brought to Quincy District Court the morning after his arrest, he was interviewed by a Dr. Levoy, a psychologist. Dr. Levoy concluded that although the defendant was responsive to questions, he was acutely mentally ill, and recommended that the defendant be referred to Bridge-water for examination. Upon his arrival at Bridgewater later that day, the defendant was, again, responsive to questions about his personal history. At the same time, however, his level of agitation was such that he had to be handcuffed or restrained in some manner. There was also concern about whether an officer should be present in his cell during any interviews.
Dr. Nestor further testified that in arriving at his opinion concerning the defendant’s lack of criminal responsibility, he had read Dr. Levoy’s report as well as a synopsis of the defendant’s records at Bridgewater, which disclosed a history of ten admissions since 1982. He also had spoken with the professionals at Bridgewater who had contact with the defendant after his admission on November 22, the defendant’s brother, and the defendant. In addition, he considered the fact that the defendant was under prescription for antipsychotic medication. Dr. Nestor testified that the defendant, at the time of the incident, had the following specific symptoms: “auditory hallucinations,” paranoidal suspicion of people, thought disorientation, difficulty controlling his emotions, trying to do so but failing, trouble taking his medications regularly, and extraordinary agitation and anger to a degree requiring some form of restraint. Dr. Nestor concluded that the defendant was acutely mentally ill on the day in question with schizo-affective disorder or bipolar disorder in acute stage, and that he would have “substantial difficulties *554conforming his behavior to the requirements of the law.”5
The trial judge rejected the defendant’s claim of lack of criminal responsibility at the time of the incident and found him guilty.6
3. Analysis. We begin our analysis with a recall of some familiar propositions. When a defendant introduces evidence that he was mentally irresponsible at the critical time in issue, the Commonwealth is put to proof of the contrary beyond a reasonable doubt. See Commonwealth v. Kostka, 370 Mass. at 527. The Commonwealth’s proof, however, need not consist of expert testimony; indeed, the proof may be made by lay testimony even in the face of uncontradicted expert testimony in the defendant’s favor. See Commonwealth v. Ricard, 355 Mass. 509, 514-515 (1969); Commonwealth v. Louraine, 390 Mass. 28, 35 (1983). It is open to the trier to take into account not only all that is entered in evidence and directed specifically to the mental condition of the defendant at the time in issue, but also evidence of his behavior in and around the episode on which he has been charged. See Commonwealth v. Cole, 380 Mass. 30, 36 (1980); Commonwealth v. Cullen, 395 Mass. at 229-230; Commonwealth v. Kappler, 416 Mass. 574, 579 (1993). The nature of the defendant’s offensive behavior, for which he has been charged, may itself have a bearing on the question of his mental condition. See Commonwealth v. LaPlante, 416 Mass. 433, 443 (1993). The trier is to criticize and assess the weight to be given expert testimony as he does with other testimony. See Commonwealth v. Kostka, 370 Mass. at 535-536; Commonwealth v. Cole, 380 Mass. at 36-37; Commonwealth v. Lunde, 390 Mass. 42, 47 (1983); Commonwealth v. Kappler, 416 Mass. at 584. And:
“In reviewing the denial of a motion for a required finding, we ‘must determine whether the Commonwealth’s *555evidence, “considered in its light most favorable to the Commonwealth, was sufficient to permit the jury to infer the existence of [criminal responsibility].” ’ Commonwealth v. Shelley, 381 Mass. 340, 346 (1980). In addition, ‘the evidence and the inferences permitted to be drawn therefrom must be “of sufficient force to bring minds of ordinary intelligence and sagacity to the persuasion of [sanity] beyond a reasonable doubt.” ’ Commonwealth v. Latimore, 378 Mass. 671, 677 (1979), quoting Commonwealth v. Cooper, 264 Mass. 368, 373 (1928).”
Commonwealth v. Kappler, 416 Mass. at 578 (emphasis added).
Notwithstanding the Commonwealth’s argument to the contrary, there is nothing in the victim’s account of the defendant’s grotesque and bizarre conduct which bespeaks sanity. Contrast Commonwealth v. Ricard, 355 Mass. at 514 (evidence of provocation that could lead a sane man to a “murderous act”); Commonwealth v. Kostka, 370 Mass. at 521 (evidence that the defendant plotted to rob store at a time when he knew only he and clerk would be present); Commonwealth v. Lunde, 390 Mass. at 48 & n. 10 (evidence of motive for the crime, understanding of Miranda warnings, subsequent concealment of weapon); Commonwealth v. Cullen, 395 Mass. at 230 (evidence that defendant shot gun deliberately rather than wildly, fled to his attorney’s home, attempted to reach for gun while struggling with police, and ultimately complied with officer’s shout to “give it up”); Commonwealth v. Kappler, 416 Mass. at 579 & n.4 (evidence of flight to New York, which, in circumstances, would permit one of two inferences indicative of sanity — consciousness of guilt or awareness of reality — and defendant’s ability to follow wife’s instruction that he admit himself to a hospital); Commonwealth v. Lo, 428 Mass. 45, 54 & n.14 (1998) (evidence of plan to commit crime and thereafter feign mental illness to avoid criminal responsibility); Commonwealth v. Werner, 16 Mass. App. Ct. 686, 689-690 (1983) (evidence that defendant hid himself and weapon after the crime, and gave detailed and coherent confession).
The Commonwealth also claims that the defendant’s ability to conform his conduct to the requirements of the law can be inferred from Rosario’s testimony that the defendant did not resist arrest and that he was responsive to booking questions concerning his personal history. Rosario’s full testimony *556concerning the circumstances of the defendant’s arrest was that at the time he and two other uniformed officers responded to the victim’s request for assistance, the defendant was being restrained by a man and offered no resistance to the three uniformed officers. Compare Commonwealth v. Cullen, 395 Mass. at 230 (trial judge could have inferred sanity from evidence of defendant’s numerous deliberate acts, including his thrashing on the ground in an attempt to reach his gun and gain an advantage on the police). Although Rosario stated that the defendant responded to booking questions, he offered no testimony concerning whether Miranda warnings were given to and understood by the defendant. Compare Commonwealth v. Lunde, 390 Mass. at 48 (defendant “responded cogently” to booking questions and thereafter, having received Miranda warnings, remained silent except to ask for an attorney).
This evidence relied upon by the Commonwealth is far less strong or persuasive than that presented in prior cases where the Commonwealth, without itself offering expert testimony, has pointed to behavior to overcome expert testimony on the side of the defendant showing a lack of responsibility. See, e.g., Commonwealth v. Ricard, 355 Mass. at 514; Commonwealth v. Lunde, 390 Mass, at 48 & n.10; Commonwealth v. Cullen, 395 Mass. at 230; Commonwealth v. Werner, 16 Mass. App. Ct. at 689-690. We conclude that any inference of sanity that could be drawn from the testimony of either the victim or Rosario is not “of sufficient force to bring minds of ordinary intelligence and sagacity to the persuasion of [sanity] beyond a reasonable doubt.”7 Commonwealth v. Kappler, 416 Mass. at 578, quoting from Commonwealth v. Latimore, 378 Mass. 671, 677 (1979).
Perhaps conscious of the thinness of its evidence, the Com*557monwealth seeks to bolster its case by invoking the presumption of sanity, that is, the formula (repeatedly stated in the cases cited throughout this opinion) that a trier is permitted to infer that a particular defendant was sane from the proposition that the great majority of people are sane. The evidential value of the presumption, however, has been held to be indeterminate. “[I]t is not... the presumption of sanity that may be weighed as evidence, but rather the rational probability on which the presumption rests.” Commonwealth v. Clark, 292 Mass. 409, 415 (1935). Standing alone, the presumption is an insufficient basis upon which to conclude that a defendant is sane beyond a reasonable doubt. See Commonwealth v. Francis, 355 Mass. 108, 111 (1969) (“Commonwealth v. Clark, at page 415, stated that in assessing a defendant’s mental responsibility for crime the jury should weigh ‘the fact that a great majority of men are sane, and the probability that any particular man is sane.’ Yet this assessment is to be made in each case in the light of the evidence introduced” [emphasis supplied]).8
That the validity of the presumption of sanity is open to serious question, because of its dependence upon a formula and supposedly inferential step which shed no true light on the question of a particular defendant’s sanity, was amply shown by Justice O’Connor, dissenting in Commonwealth v. Kappler, 416 Mass. at 588, 599-601.9 There, however, the court determined *558that it need not confront the question of the continued use of the formula as evidence because it concluded that there was sufficient evidence in the case, apart from the presumption, to establish the defendant’s sanity beyond a reasonable doubt. Id. at 588-589 & n.l.10
That is not the situation in the instant case. We have concluded that the evidence concerning the defendant’s actions during and following the act in issue does not permit an inference “of sufficient force to bring minds of ordinary intelligence and sagacity to the persuasion of [sanity] beyond a reasonable doubt.” Commonwealth v. Kappler, 416 Mass. at 578 (citation omitted). It follows from that conclusion that this same evidence cannot provide a sufficient basis to give a presumption of questionable and indeterminate evidential value the weight necessary to affirm a conviction which we otherwise, in justice, would reverse. The Commonwealth’s evidence, even when considered in the light of any benefit which the presumption of sanity might be deemed to provide, leaves the issue of the defendant’s sanity to conjecture and surmise and, therefore, the guilty verdict cannot stand.
4. Conclusion. It follows from what we have said that the judgment is reversed, the finding is set aside, and the case is remanded to the District Court for entry of a judgment of acquittal by reason of the defendant’s lack of criminal responsibility.
So ordered.
McHoul adopts § 4.01 of the American Law Institute’s Model Penal Code, Proposed Official Draft (1962): “Mental Disease or Defect Excluding Responsibility. (1) A person is not responsible for criminal conduct if at the *551time of such conduct as a result of mental disease or defect he lacks substantial capacity either to appreciate the criminality [wrongfulness] of his conduct or to conform his conduct to the requirements of law.” 352 Mass. at 546-547.
As there explained:
“In cases where the question of insanity is raised, as in the instant case, the facts underlying the presumption and the inference that may be drawn from those facts provide a basis for the jury to determine that the defendant was sane beyond a reasonable doubt at the time the crime was committed. In this sense, the ‘presumption of sanity’ is merely an expression we have used to describe both ‘the fact that a great majority of men are sane,’ Commonwealth v. Clark, 292 Mass. 409, 415 (1935), and the ‘probability that any particular man is sane,’ id., from which the jury may conclude that the defendant is sane.”
Because there is no dispute that the defendant committed the act set out in *552the complaint, consideration of a request for a required finding of not guilty at the close of the Commonwealth’s case would have been inappropriate. See Commonwealth v. Kappler, 416 Mass. 574, 578 n.2 (1993).
Although the records from Bridgewater were not introduced into evidence, much of their content appears in the transcript by reason of the questioning of Dr. Nestor. The transcript also shows that the prosecutor never challenged the accuracy of the factual data reported in the records and, instead, focused only upon the validity of the expert’s opinion.
Dr. Nestor also opined that the defendant’s actions on the day in question could have been precipitated by his agitation upon discovering that he had boarded the Braintree rather than the Ashmont train.
That same day, February 20, 1997, the trial judge sentenced the defendant to two years incarceration, six months to serve (with credit for ninety-two days time served), the balance suspended to February 16, 1999, with conditions of psychiatric evaluation, continued medication, treatment deemed necessary through evaluation, and supervision by the Department of Mental Health.
The Commonwealth makes no argument that there are facts in Dr. Nestor’s testimony which would support an inference of sanity. Instead, it argues that his testimony is flawed in three respects: (1) it lacks explanation of how the defendant’s mental disease operated to produce the claimed irresponsibility; (2) it is based, in part, upon interviews with the defendant who, having been given his warnings pursuant to Commonwealth v. Lamb, 365 Mass. 265, 270 (1974), might have tailored his statements to the expert accordingly; and (3) it shows that the expert declined to render an opinion until the defendant spoke with his attorney, his reluctance to do so earlier based upon the fact that the defendant’s “perceptions were so clouded by the mental illness that he’s experienced at that time” that he (the expert) wanted confirmation of whether the act, in fact, had been committed to avoid any “logical inconsistency” in finding that the defendant was “not responsible for something that might not *557have happened.”
Any deficiencies in the expert’s testimony, however, add nothing to the Commonwealth’s evidence.
Moreover, were the presumption of sanity sufficient in and of itself to satisfy the Commonwealth’s burden of proving sanity beyond a reasonable doubt, a required finding of not guilty by reason of insanity would be unavailable, as matter of law, to a defendant claiming a lack of criminal responsibility. However, such a proposition is refuted by those decisions wherein the sufficiency of the Commonwealth’s evidence to overcome a request for a required finding is analyzed. See, e.g., Commonwealth v. Kostka, 370 Mass, at 521-522; Commonwealth v. Cullen, 395 Mass, at 230; Commonwealth v. Kappler, 416 Mass, at 579 & n.4.
In his dissent, Justice O’Connor quotes the familiar passage from Sargent v. Massachusetts Accident Co., 307 Mass. 246, 250 (1940): “[F]or example, the fact that colored automobiles made in the current year outnumber black ones would not warrant a finding that an undescribed automobile of the current year is colored and not black, nor would the fact that only a minority of men die of cancer warrant a finding that a particular man did not die of cancer.” 416 Mass, at 600. See Tribe, Trial by Mathematics: Precision and Ritual in the Legal Process, 84 Harv. L. Rev. 1329, 1334-1338 (1971), citing People v. Collins, 68 Cal. 2d 319 (1968).
Justice Abrams, concurring in Commonwealth v. Kappler, 416 Mass. at 601-602, after noting the difficulties that arise when the prosecution carries the burden of proving sanity, wrote in favor of a change in the law to place the burden of proving insanity upon the defendant and thus eliminating the need for an instruction on the presumption of criminal responsibility.